Green’s Dictionary of Slang

off like a... phr.

[SE off, away + pun on off, stale]

In phrases

off like a bride’s nightie (also off like a prom dress, up and down like a bride’s nightie)

(Aus./US campus) leaving or acting extremely fast, very speedily.

[Aus]B. Humphries Traveller’s Tool 36: The economy is up and down like a bride’s nightie.
[Aus]Good Times (Canberra) 17 Apr. 1/1: One would expect most to be off like a bride’s nightie, but no, many were keen to talk .
[Aus]R.G. Barrett Boys from Binjiwunyawunya 59: ‘We are off this time, are we,’ asked Les. ‘Like a bride’s nightie’.
[US]Eble Campus Sl. Fall 6: off like a prom dress – leave.
[US]Eble Campus Sl. Apr. 7: off like a prom dress – comment that the speaker is about to leave.
[NZ]McGill Reed Dict. of N.Z. Sl. 146: off like a bride’s nightie/a larrikin’s hat in a high wind [...] Swift departure. ANZ mid C20.
[Aus]Australian (Sydney) 4 Aug. 3: [headline] Fugitive off like a bride’s nightie.
off like a bucket of prawns in the (hot) sun [pun on SE off, stale]

(Aus.) leaving very quickly.

Olivet Nazarene University [Internet] [heading] We’re off like a Bucket of Prawns in the Hot Sun to Australia.
S. Gerrish ‘The Gulf Run Story’ at wamperth.tripod.com [Internet] Stacey’s arm only needs a plaster cast so we’re off like a bucket of prawns in the sun and after lunch and a tyre pressure check at Dalby, we make our first camp at a roadside stop.
buffalogames.com [Internet] Thawing out on this hole sometimes requires a 3-wood off the tee to clear the Tasman Sea. A long iron into the outback and a wedge into the green should have you off like a bucket of prawns in the sun.
off like a robber’s dog

(Aus.) leaving very quickly.

[Aus]B. Hudson First Aus. Dict. Vulgarities & Obscenities n.p.: Off Rapid or swift. ... Off like a robber’s dog.
[Aus]J. Lambert Macquarie Book of Slang 202/2: robber’s dogphr.. a dog such as would be owned by a petty thief, used as a metaphor for a. speed: off like a robber’s dog; run like a robber’s dog.
[NZ]McGill Reed Dict. of N.Z. Sl. 146: off like a bride’s nightie/a larrikin’s hat in a high wind/a robber’s dog [...] Swift departure. ANZ mid C20.
off like grandma’s pants on payday

(Aus.) very fast.

[Aus]T. Spicer Good Girl Stripped Bare 8: This is a Queensland expression, used in such circumstances. It’s up there with [...] ‘off like grandma’s pants on payday’.